What is the Greatest Common Factor of 1200 and 1210?

Greatest common factor (GCF) of 1200 and 1210 is 10.

GCF(1200,1210) = 10

We will now calculate the prime factors of 1200 and 1210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1200 and 1210.

How to find the GCF of 1200 and 1210?

We will first find the prime factorization of 1200 and 1210. After we will calculate the factors of 1200 and 1210 and find the biggest common factor number .

Step-1: Prime Factorization of 1200

Prime factors of 1200 are 2, 3, 5. Prime factorization of 1200 in exponential form is:

1200 = 2⁴ × 3¹ × 5²

Step-2: Prime Factorization of 1210

Prime factors of 1210 are 2, 5, 11. Prime factorization of 1210 in exponential form is:

1210 = 2¹ × 5¹ × 11²

Step-3: Factors of 1200

List of positive integer factors of 1200 that divides 1200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600

Step-4: Factors of 1210

List of positive integer factors of 1210 that divides 1200 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1200 and 1210. The biggest common factor number is the GCF number.
So the greatest common factor 1200 and 1210 is 10.

Also check out the Least Common Multiple of 1200 and 1210